%I
%S 0,1,2,0,1,0,2,0,1,2,0,2,1,0,1,2,0,1,0,2,0,1,3,0,1,0,2,0,1,0,3,0,1,0,
%T 2,0,1,2,0,2,1,0,1,2,0,1,0,2,0,1,2,0,2,1,0,1,3,0,1,0,2,0,1,0,3,0,1,0,
%U 2,0,1,2,0,2,1,0,1,2,0,1,0,2,0,1,2,0,2
%N Lexicographically earliest sequence of nonnegative integers such that for any n > 0, the palindromic word (a(n), a(n1), ..., a(1), a(0), a(1), ..., a(n1), a(n)) is squarefree.
%C A word is squarefree if it has no subsequence of the form XX.
%C This sequence has similarities with A007814, the lexicographically earliest squarefree sequence of nonnegative integers.
%C Is this sequence unbounded?
%H Rémy Sigrist, <a href="/A309011/a309011.txt">C program for A309011</a>
%e For n = 0:
%e  a(0) = 0.
%e For n = 1:
%e  "000" is not squarefree,
%e  "101" is squarefree,
%e  hence a(1) = 1,
%e For n = 2:
%e  "01010" is not squarefree,
%e  "11011" is not squarefree,
%e  "21012" is squarefree,
%e  hence a(2) = 2,
%e For n = 3:
%e  "0210120" is squarefree,
%e  hence a(3) = 0.
%o (C) See Links section.
%Y Cf. A007814.
%K nonn
%O 0,3
%A _Rémy Sigrist_, Jul 06 2019
